Answer:
[tex]D=9\sqrt{2}\ in[/tex]
Step-by-step explanation:
step 1
Find out the length side of the square
we know that
The perimeter pf the square is equal to
[tex]P=4b[/tex]
where
b is the length side of the square
we have
[tex]P=36\ in[/tex]
so
[tex]36=4b[/tex]
Solve for b
[tex]b=36/4\\b=9\ in[/tex]
step 2
Find out the length of the diagonal applying the Pythagoras Theorem
Let
D -----> the length of the diagonal of the square
b ----> the length side of the square
we have that
[tex]D^2=b^2+b^2[/tex]
we have
[tex]b=9\ in[/tex]
substitute
[tex]D^2=9^2+9^2[/tex]
[tex]D^2=2(81)[/tex]
[tex]D=\sqrt{162}\ in[/tex]
Simplify
[tex]D=9\sqrt{2}\ in[/tex]
